EAs can and will do whatever they like to sell to their mates or obstruct viewers from getting through your door. It's only when they receive an offer that they have a legal obligation to put that forward to you.
Because my life isn't nearly tedious enough right now, I watch quite a lot of estate agent shows on a semi regular basis. One of the common themes coming through in the last few months is 'your people really need to be pushing extras because our sales numbers are down and the bottom line is not going to look good otherwise' (ergo, job losses will start to happen). Their extras may include: getting the seller to do an EPC through their recommended person, getting the buyer to use their conveyancer, their mortgage broker, their surveyors. Only accepting viewings from a buyer who also has a house to sell (so bolsters what they have on their books).
I'm not saying your EA is refusing to let anyone view who says they don't want to use them for any of the above services, but it IS a thing that happens. They get quite sizeable commission from all of the above, and that will bolster their 2023 commission figures quite quickly (bear in mind they could be waiting 4-6 months for a sales commission to come through).
Sadly, I think you might just be in a perfect storm of wrong timing: the post-summer house buying boom didn't happen this year, now it's getting to the time of year when people won't really be looking because nobody can now really logistically move before Christmas, so who wants to have the stress of dealing with a purchase and potentially ruining their own xmas if things start falling apart between now and January. Also, your EA doesn't sound great. Plus you said several others have sold recently, so maybe that's used up all the local buying pool who can afford homes like yours, for the time being.
But having read your additional posts on here, I'd say the primary problem is your house is a FTB house in a market where 'the number of FTBs calling us about mortgages has dropped off a cliff edge' - recent mortgage broker anecdotal stories.